According to Trinitarianism, is it valid to pray to God "in general" (the whole Godhead) without specifying the Person (Father, Son or Holy Spirit), or should we always be explicit about which Person we are specifically directing the prayer to?
Jesus taught his disciples how to pray:
Pray then like this: “Our Father in heaven, hallowed be your name... (Matthew 6:9)
In other words, we pray to God the Father (Abba, Father).
“Hallowed be your name” tells us to worship God, and to praise Him for who He is.
Since there has only ever been the One Being of God, in whom subsist the three personages of Father, Son and Holy Spirit, when we pray to God we are praying to all three.
Our prayers are specifically directed to God the Father. We pray in the name of Jesus, and it is the power of the Holy Spirit that intercedes for us when we struggle to know how to express ourselves:
In the same way, the Spirit helps us in our weakness. We do not know what we ought to pray for, but the Spirit himself intercedes for us with groans that words cannot express. And he who searches our hearts knows the mind of the Spirit, because the Spirit intercedes for the saints in accordance with God's will. (Romans 28:26-27)
When I pray to the Father, I remember to always thank Him for the greatest gift possible, that of His Son, and also to thank Him for the Holy Spirit which He sent to help us. However, I address my prayer specifically to our Father God in heaven.